1. Evaluate: a) S x³ sec-1(ln (x)) dx

Q: dx Perform the Integrations 1+ sin x+ cos x

A:

Q: Evaluate e sin x cos x dx using Simpson rule with h 20

A:

Q: Compute cosh x and tanh x, assuming that sinh x = 0.8.

A: Here given as sinhx=0.8 Use the identity…

Q: Evaluate the integral (exact value). e2X sin(8x) dx =

A: We have to find the integral.

Q: S.Si dx dy о 1+ху

A:

Q: sinh x dx 1+ cosh x

A:

Q: -Vx+ 1+ In(x) e* lim + sin (x)cos(x)

A: Find the limit

Q: I = | In(ax + 1) dx, for a > 0

A: Find the integration of I

Q: Evaluate / x cos(128x)dx. Use capital C for your constant of integration.

A:

Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

A:

Q: Find the equation of tangent at x = In 5: ln 2x a) y = ²x + 1 e to :

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Which of the following is correct? " 17 3 (3 sinh-(x)) = (coth"(x) = (지 < 1) V - 1 dx Option 1…

A:

Q: Use x = ey to explain why d/dx (ln x) = 1/x, for x &gt; 0.

A:

Q: Se* sin e*dx

A: We have to find integrating of given Questions

Q: Solve dx dy for y= sec (In x) In (tan x)

A:

Q: sinh In(2+2x) dx? x+1

A:

Q: A-The derivative is y = ln sin 0 cos 0 1+2ln 0

A:

Q: Solve th D.E using Exact dx +(x² +3y* )dy

A:

Q: 2*csch( 2*) d x cosh(2*)-sinh(2*)

A:

Q: Li S cos(x)esin(x)-2y dxdy

A:

Q: xe2X sin(e)dx 2x2

A: As per guideline we have to solve only one

Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: Find if y = e* In(sinh x) dx

A:

Q: Differentiate the following finction f(x)=sin(3 ln(x))

A: Given that the function is       f(x) = sin(3 ln(x)) We have to differentiate the the function f(x).

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your du? du = x…

A:

Q: Jrin m In(cos m) dm

A:

Q: A-The derivative is y = In sin 0 cos 0 1+2 ln 0

A:

Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

A:

Q: In integrating the function fx In 5x dx using integration by parts, what would be your v?

A:

Q: (a) Find thne derivative. y = In(4x – 6) – 3 In(x) dy dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the length of y = ln (sec x) between x = 0 to x = π/4.

A: you meant to find the arc length of y=ln(secx). the formula for the length of the arc in the given…

Q: Find dy/dx by implicit differentiation

A: Given function

Q: Solve the definite integral ro e(arcsin(x)) dx. V1 - x2

A:

Q: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: Evaluate the integral. sinh 5a -dx +C. 5x

A: Evaluate the integral the given function Sinh is hyperbole function.

Q: 1. Sx arctan x? dx =x² arctan(x²) – In(1 + x*) + C

A:

Q: dy/dx for (ln(tan(2x)-sqrt(3+e^2x) / (pi(x)^3-cos^2(-5x))

A: Given,     y  =  ln(tan2x)-3+e2xπx3-cos2(-5x)

Q: 1 B3. Evaluate dx, using substitution method.

A:

Q: Solve the definite integral e(arcsin(x)) dx. /1 – x²

A:

Q: Determine the equation of the tangent line to the x³ + ln x graph of f(x) = sil 3 3 + 5tº dt at x =…

A:

Q: 4) [ sinh 2xdx 5) [ e* sin e"dx 6) fcosh'vdv

A: Given:  4) ∫0π2 sinh(2x)dx5) ∫ln(π)2exsinexdx6) ∫cosh2vdv

Q: Show that d/dx(ln kx) = d/dx(ln x), where x &gt; 0 and k is a positivereal number

A:

Q: (b) Evaluate the integral sec X dx J sec x- cosX

A: To evaluate the given integral

Q: Se Sin (3x) dx by Improper htegrations.

A: use improper integral

Q: Calculate the exact value of the intergral ∫ln(x)dx where b = 3 and a = 1

A:

Q: A-The derivative is y = In Vsin 0 cos 0 1 + 2 ln 0

A: Let's find derivative of given  function.

Q: Cualuate the definle integial. x33 COs (xH) dx

A:

Q: arc sin z = -i log(iz + V1- 22).

A: